What kind of network your time series becomes when you connect every pair of points that can "see" each other over the intervening values.
Treats the signal as a landscape and draws an edge between two time points whenever no intermediate value blocks the line of sight between them. Tall peaks see far; valleys are hidden. The resulting graph's degree distribution, clustering, and assortativity encode the signal's dynamical class. Periodic signals produce regular graphs. Chaotic signals produce scale-free networks. Random signals produce specific power-law exponents predicted by theory.
Do high-degree nodes connect to other high-degree nodes (positive), or to low-degree ones (negative)? Rössler Hyperchaos (0.76) is strongly assortative: its tall peaks cluster together. LIGO Livingston (0.54) also shows this pattern. Lotka-Volterra (-0.57) is strongly disassortative: its predator-prey oscillations create peaks that connect to valleys, not to each other. Logistic Period-2 (-0.50) alternates high-low, producing the same disassortative pattern.
How interconnected are each node's neighbors? Rainfall (0.85) has the highest clustering -- its rain events create local clusters of mutually visible points. Neural Net Pruned (0.83) and Sensor Event Stream (0.81) show similar cliquish structure. Devil's Staircase (0.0) has zero clustering because its flat plateaus followed by jumps create a graph where neighbors never see each other.
Power-law exponent of the degree distribution. DNA SARS-CoV-2 (2.94) has the steepest decay -- most nodes have low degree, with rare high-degree hubs. Circle Map QP (2.78) and Rule 30 (2.77) follow. For iid random data, the NVG degree distribution is exponential (Lacasa et al. 2008), so the power-law exponent from a forced fit is not theoretically meaningful in that regime — but deviations across signals still reveal structural differences.
The most-connected node in the graph. Lotka-Volterra (690) has an extreme hub -- its largest predator-prey peak can see across 690 other time points. Rainfall (587) and Van der Pol (540) also produce high-visibility peaks. Devil's Staircase has max_degree = 2, meaning no point can see beyond its immediate neighbors.
| Source | Domain | Value |
|---|---|---|
| Rössler Hyperchaos | chaos | 0.7641 |
| LIGO Livingston | astro | 0.5444 |
| Clipped Sine | waveform | 0.4930 |
| ··· | ||
| Lotka-Volterra | bio | -0.5740 |
| Logistic r=3.2 (Period-2) | chaos | -0.4966 |
| Hodgkin-Huxley | bio | -0.4472 |
| Source | Domain | Value |
|---|---|---|
| Rainfall (ORD Hourly) | climate | 0.8524 |
| Neural Net (Pruned 90%) | binary | 0.8301 |
| Sensor Event Stream | exotic | 0.8123 |
| ··· | ||
| Constant 0xFF | noise | 0.0000 |
| Constant 0x00 | noise | 0.0000 |
| Devil's Staircase | exotic | 0.0000 |
| Source | Domain | Value |
|---|---|---|
| DNA SARS-CoV-2 | bio | 2.9429 |
| Circle Map Quasiperiodic | chaos | 2.7779 |
| Rule 30 | exotic | 2.7720 |
| ··· | ||
| Constant 0xFF | noise | 0.0000 |
| Constant 0x00 | noise | 0.0000 |
| Devil's Staircase | exotic | 0.0000 |
| Source | Domain | Value |
|---|---|---|
| Earthquake Depths | geophysics | 0.9743 |
| Poker Hands | exotic | 0.9630 |
| Collatz Stopping Times | number_theory | 0.9613 |
| ··· | ||
| Constant 0xFF | noise | 0.0000 |
| Constant 0x00 | noise | 0.0000 |
| Devil's Staircase | exotic | 0.0000 |
| Source | Domain | Value |
|---|---|---|
| Sine Wave | waveform | 0.1564 |
| Lotka-Volterra | bio | 0.1451 |
| Duffing Oscillator | chaos | 0.1366 |
| ··· | ||
| Constant 0xFF | noise | 0.0000 |
| Constant 0x00 | noise | 0.0000 |
| Devil's Staircase | exotic | 0.0020 |
| Source | Domain | Value |
|---|---|---|
| Lotka-Volterra | bio | 690.4000 |
| Rainfall (ORD Hourly) | climate | 587.4000 |
| Van der Pol Oscillator | exotic | 539.8000 |
| ··· | ||
| Constant 0xFF | noise | 0.0000 |
| Constant 0x00 | noise | 0.0000 |
| Devil's Staircase | exotic | 2.0000 |
Visibility Graph is the atlas's best tool for separating oscillatory dynamics by their waveform shape. The assortativity metric spans from -0.57 to +0.76 across the atlas, a range no other metric covers, and it cleanly separates predator-prey / period-doubling dynamics (negative) from hyperchaotic / bursty dynamics (positive). The clustering coefficient uniquely identifies bursty event streams and rainfall as topologically cliquish -- a property invisible to spectral or distributional geometries.